1.Peter Stone is considering buying a $100 face value, semi-annual coupon bond with a quoted price of 105.19. His colleague points out that the bond is trading ex-coupon. Which of the following choices best represents what Stone will pay for the bond?
 
　　A. $105.19 plus accrued interest.
 
　　B. $105.19.
 
　　C. $105.19 minus accrued interest.
 
　　D. $105.19 minus the coupon payment.
 
　　2.Which of the following bonds may have negative convexity:
 
　　A. Mortgage backed securities.
 
　　B. High yield bonds.
 
　　C. All of these choices are correct.
 
　　D. Callable bonds.
 
　　3.Consider the delta-normal and full-revaluation approaches to estimating the VAR of non-linear derivative instruments. Which of the following is NOT a requirement for either the delta-normal or full-revaluation approach?
 
　　A. The VAR(1%) of the underlying asset is adjusted by a factor reflecting the price sensitivity of the derivative price to changes in the underlying asset price.
 
　　B. A second order adjustment is made to the underlying asset VAR(1%) to account for the non-linear relationship between the derivative and the underlying asset.
 
　　C. The VAR(1%) of the derivative is calculated by revaluing the derivative at the price corresponding to a VAR(1%) decline in the value of the underlying asset.
 
　　D. The VAR(1%) of the asset underlying the derivative is based on an assumed normal distribution.
 
　　Answer:
 
　　1.B
 
　　Since the bond is trading ex-coupon, the buyer will pay the seller the clean price, or the price without accrued interest. So, Stone will pay the quoted price. The choice $105.19 plus accrued interest represents the dirty price (also known as full price). This bond would be said to trade cum-coupon.
 
　　2.C
 
　　Negative convexity is the idea that as interest rates decrease they get to a certain point where the value of certain bonds (bonds with negative convexity) will start to increase in value at a decreasing rate.
 
　　Interest rate risk is the risk of having to reinvest at rates that are lower than what an investor is currently receiving.
 
　　Mortgage backed securities (MBS) may have negative convexity because when interest rates fall mortgage owners will refinance for lower rates, thus prepaying the outstanding principal and increasing the interest rate risk that investors of MBS may incur.
 
　　Callable bonds are similar to MBS because of the possibility that the principal is being returned to the investor sooner than expected if the bond is called causing a higher level of interest rate risk.
 
　　High yield bonds may exhibit negative convexity because they are lower quality bonds with large coupon payments thus causing a larger potential for interest rate risk when interest rates fall because the investor has to reinvest their cash flows at a lower interest rate which is similar to both MBS and callable bonds.  High yield issuers would be more prone to refinancing their debt as interest rates fall since they pay an initially high rate of interest and would greatly benefit by refinancing.
 
　　3.D
 
　　The delta-normal approach to estimating the VAR of a non-linear derivative adjusts the VAR of the underlying asset for the delta (slope) and gamma (curvature) of the relationship between the derivative and the underlying. The VAR of the underlying asset can be calculated using parametric methods (assuming a normal distribution) or using historical methods (which does not assume a normal distribution).

 
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